The stabilities of $(BN)_x(C_2)_{1-x}$ alloys and related superlattices are investigated by ab initio pseudopotential calculations. We find that the $(BN)_1/(C_2)_1$ superlattices in (111) orientations have the lowest formation energy among many short-range ordered $BNC_2$ structures due to the smallest number of B-C and C-N bonds. Based on the calculated formation energies at several compositions and for various ordered structures and assuming thermodynamic equilibrium, the solid solution phase diagram of $(BN)_x(C_2)_{1-x}$ alloys is constructed. We find that the complete miscibility of $(BN)_x(C_2)_{1-x}$ alloys is possible, which is in contrast with previous theoretical predictions but in agreement with experimental reports.
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